Answer:
The speed of the particle at t = 6 is 4 units per second
Explanation:
The problem states that a particle moves along the x-axis so that at time t > 0, its position is given by x(t) = -t² + 4t + 27. We are asked to determine the speed of the particle at t = 6.
To determine the speed of the particle, we need to find the derivative of the position function x(t) with respect to time t. This derivative represents the particle's velocity v(t).
x(t) = -t² + 4t + 27
v(t) = dx/dt = -2t + 4
Now, we can plug in t = 6 into the velocity function to find the particle's speed at that time:
v(6) = -2(6) + 4 = -8 + 4 = -4
Therefore, the speed of the particle at t = 6 is 4 units per second. Since the velocity is negative, we know that the particle is moving in the negative direction along the x-axis.